(x-1)(x-2)=(3x+2)(3-x)+2

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Solution for (x-1)(x-2)=(3x+2)(3-x)+2 equation: 


Simplifying
(x + -1)(x + -2) = (3x + 2)(3 + -1x) + 2

Reorder the terms:
(-1 + x)(x + -2) = (3x + 2)(3 + -1x) + 2

Reorder the terms:
(-1 + x)(-2 + x) = (3x + 2)(3 + -1x) + 2

Multiply (-1 + x) * (-2 + x)
(-1(-2 + x) + x(-2 + x)) = (3x + 2)(3 + -1x) + 2
((-2 * -1 + x * -1) + x(-2 + x)) = (3x + 2)(3 + -1x) + 2
((2 + -1x) + x(-2 + x)) = (3x + 2)(3 + -1x) + 2
(2 + -1x + (-2 * x + x * x)) = (3x + 2)(3 + -1x) + 2
(2 + -1x + (-2x + x2)) = (3x + 2)(3 + -1x) + 2

Combine like terms: -1x + -2x = -3x
(2 + -3x + x2) = (3x + 2)(3 + -1x) + 2

Reorder the terms:
2 + -3x + x2 = (2 + 3x)(3 + -1x) + 2

Multiply (2 + 3x) * (3 + -1x)
2 + -3x + x2 = (2(3 + -1x) + 3x * (3 + -1x)) + 2
2 + -3x + x2 = ((3 * 2 + -1x * 2) + 3x * (3 + -1x)) + 2
2 + -3x + x2 = ((6 + -2x) + 3x * (3 + -1x)) + 2
2 + -3x + x2 = (6 + -2x + (3 * 3x + -1x * 3x)) + 2
2 + -3x + x2 = (6 + -2x + (9x + -3x2)) + 2

Combine like terms: -2x + 9x = 7x
2 + -3x + x2 = (6 + 7x + -3x2) + 2

Reorder the terms:
2 + -3x + x2 = 6 + 2 + 7x + -3x2

Combine like terms: 6 + 2 = 8
2 + -3x + x2 = 8 + 7x + -3x2

Solving
2 + -3x + x2 = 8 + 7x + -3x2

Solving for variable 'x'.

Reorder the terms:
2 + -8 + -3x + -7x + x2 + 3x2 = 8 + 7x + -3x2 + -8 + -7x + 3x2

Combine like terms: 2 + -8 = -6
-6 + -3x + -7x + x2 + 3x2 = 8 + 7x + -3x2 + -8 + -7x + 3x2

Combine like terms: -3x + -7x = -10x
-6 + -10x + x2 + 3x2 = 8 + 7x + -3x2 + -8 + -7x + 3x2

Combine like terms: x2 + 3x2 = 4x2
-6 + -10x + 4x2 = 8 + 7x + -3x2 + -8 + -7x + 3x2

Reorder the terms:
-6 + -10x + 4x2 = 8 + -8 + 7x + -7x + -3x2 + 3x2

Combine like terms: 8 + -8 = 0
-6 + -10x + 4x2 = 0 + 7x + -7x + -3x2 + 3x2
-6 + -10x + 4x2 = 7x + -7x + -3x2 + 3x2

Combine like terms: 7x + -7x = 0
-6 + -10x + 4x2 = 0 + -3x2 + 3x2
-6 + -10x + 4x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
-6 + -10x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -5x + 2x2) = 0

Factor a trinomial.
2((-1 + -2x)(3 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1 + -2x)' equal to zero and attempt to solve:

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + -2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2x = 0 + 1
-2x = 0 + 1

Combine like terms: 0 + 1 = 1
-2x = 1

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-0.5, 3}

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